Quantum mechanics

Engineering

Service (business)

Statistics

Spline (mechanical)

Differential equation

Applied mathematics

Convergence (economics)

Stability (learning theory)

Economics

Computer science

Collocation method

Thermodynamics

Physics

Collocation (remote sensing)

Diffusion

Error analysis

Mathematics

Bilinear interpolation

Spline interpolation

Orthogonal collocation

Mathematical analysis

Geometry

Ordinary differential equation

Thin plate spline

Structural engineering

Polygon mesh

Economy

Economic growth

Diffusion equation

Finance

Term (time)

Order (exchange)

Machine learning

Computers & Mathematics with Applications

In this paper, we consider an orthogonal spline collocation (OSC) method to solve the fourth-order multi-term subdiffusion equation. The L1 method on graded meshes is employed in temporal direction. In the spatial direction, we develop the orthogonal spline collocation method. The stability and convergence of the above mentioned method are proved theoretically, and it's still valid if α1→1−. A new robust error bound is obtained, which is a more natural and desirable result and does not blow up as α1→1−. Some numerical results are also provided to verify our theoretical analysis and demonstrate the effectiveness of the OSC method.

A robust error analysis of the OSC method for a multi-term fourth-order sub-diffusion equation